Final answer:
To simplify the expression 24x⁶ + y⁻³ / 12x⁻⁸ - y⁷, combine like terms and simplify the fractions. The simplified form is 24x¹⁴y⁷ + x⁸y⁴ / 12x⁸y⁷ - x⁸y¹⁴.
Step-by-step explanation:
To simplify the expression 24x⁶ + y⁻³ / 12x⁻⁸ - y⁷, we can combine like terms and simplify the fractions.
First, let's simplify the numerator:
24x⁶ + y⁻³ = 24x⁶ / 1 + y⁻³ / 1 = 24x⁶ + 1/y³
Next, let's simplify the denominator:
12x⁻⁸ - y⁷ = 12/x⁸ - 1/y⁷
Now we can simplify the entire expression:
(24x⁶ + 1/y³) / (12/x⁸ - 1/y⁷)
To simplify further, we can multiply the numerator and denominator by the least common multiple (LCM) of the denominators, which is x⁸y⁷:
(24x⁶ * x⁸y⁷ + (1/y³) * x⁸y⁷) / (12/x⁸ * x⁸y⁷ - 1/y⁷ * x⁸y⁷)
This becomes:
24x¹⁴y⁷ + x⁸y⁴ / 12x⁸y⁷ - x⁸y¹⁴
And that's the simplified form of the expression.